Modeling variable density flow in subsurface and surface water in the vicinity of the boundary between a surface water-atmosphere system and the subsurface.

When seawater intrudes into a subterranean estuary, there is interaction between groundwater and surface water, and ocean tides and waves can influence the salt concentration distribution in subsurface of the estuary. However, numerical simulations of seawater intrusion into a subterranean estuary often neglect the atmosphere and surface water and simply specify hydrostatic pressure and a constant seawater salt concentration. This study examined the influence of fluid flow and pressure in a surface water-atmosphere system consisting of both atmosphere and surface water on the salt distribution in subsurface and in the surface water by a numerical simulation that couples fluid flows in the surface water-atmosphere system and groundwater. This study first confirmed the precision of the simulation method by comparing experimentally determined salt concentration distributions in silica beads unsaturated with water. This study then conducted an experiment in a two-dimensional tank filled with seawater and glass beads (mean diameter 0.2 mm) and carried out two simulations of this tank experiment: one of a limited system consisting of the porous medium and surface water only, and the other of a full system, consisting of the porous medium, surface water, and atmosphere. Darcy's law has frequently been applied in limited system simulations by assigning extremely high permeability to the surface water. This study therefore also conducted a third, simpler numerical simulation of the limited system that used only Darcy's law. The salt concentration distribution obtained by the full system simulation was closer to the experimental distribution than that obtained by the limited system simulation. This result implies that fluid flow and pressure in both the atmosphere and surface water influence water flow and water pressure in the porous medium. Furthermore, the third simulation using Darcy's law only could not precisely reproduce flow in the surface water. Therefore, when variable-density flow in surface water and a shallow subsurface are numerically simulated, the simulation system needs to include atmosphere and surface water to take account of the influence of fluid flow and fluid pressure in both the atmosphere and surface water on the fluid flow and transport of salt in a shallow subsurface.

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Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.